If the job is only being done for cosmetic reasons, and can’t be moved, frame around the stove with metal 2x on end, attach backer to it, and then tile up to and over the backer. Actually, you could put it on side and the backer plus tile would bring it up 2”. The stove has not been moved. You can’t see under it, so you don’t have to worry about it. There’s just an attractive raised border around the stove.
